import numpy as np

from trainLinearReg import trainLinearReg
from linearRegCostFunction import linearRegCostFunction

def learningCurve(X, y, Xval, yval, Lambda):
    """returns the train and
    cross validation set errors for a learning curve. In particular,
    it returns two vectors of the same length - error_train and
    error_val. Then, error_train(i) contains the training error for
    i examples (and similarly for error_val(i)).

    In this function, you will compute the train and test errors for
    dataset sizes from 1 up to m. In practice, when working with larger
    datasets, you might want to do this in larger intervals.
    """

# Number of training examples
    m, _ = X.shape

# You need to return these values correctly
    error_train = np.zeros(m)
    error_val   = np.zeros(m)

# ====================== YOUR CODE HERE ======================
# Instructions: Fill in this function to return training errors in 
#               error_train and the cross validation errors in error_val. 
#               i.e., error_train(i) and 
#               error_val(i) should give you the errors
#               obtained after training on i examples.
#
# Note: You should evaluate the training error on the first i training
#       examples (i.e., X(1:i, :) and y(1:i)).
#
#       For the cross-validation error, you should instead evaluate on
#       the _entire_ cross validation set (Xval and yval).
#
# Note: If you are using your cost function (linearRegCostFunction)
#       to compute the training and cross validation error, you should 
#       call the function with the lambda argument set to 0. 
#       Do note that you will still need to use lambda when running
#       the training to obtain the theta parameters.
#
# Hint: You can loop over the examples with the following:
#
#       for i = 1:m
#           # Compute train/cross validation errors using training examples 
#           # X(1:i, :) and y(1:i), storing the result in 
#           # error_train(i) and error_val(i)
#           ....
#           
#       end
#

# ---------------------- Sample Solution ----------------------



# -------------------------------------------------------------------------

# =========================================================================

    return error_train, error_val